Calculation of integral coefficients in the correlation magnetodynamics equations for a ferromagnet

The equations of Correlation Magnetodynamics (CMD) are an extension of the traditional Landau–Lifshitz–Bloch equation and aim to provide the most comprehensive continuum model of a magnet, accounting for the nonstationary influence of temperature. The main challenge in constructing CMD lies in calculating the integral coefficients — higher-order moments of two- and three-particle distribution functions of a classical Heisenberg magnet (a system of magnetic moments with arbitrary orientations, coupled by exchange interaction). In this work, we present analytical expressions for the partition function of such distribution functions, which allow for the computation of CMD coefficients and provide significantly better insight into the approximations made in the construction of CMD.